DR. JAMES GRIME: Have you ever
heard of the time when they tried to redefine pi,
to redefine pi so that it was 3.2? BRADY HARAN: I'm about to. DR. JAMES GRIME: Yes, you are. This is absolutely insane. It's a true story, as well. And it's absolutely crazy. So this happened-- well, I don't think
that long ago. It was 1897. And there was a guy called Edwin
Goodwin, this amateur mathematician who thought he had
solved one of the unsolved problems of mathematics, a
problem that goes way back to ancient Greece. It was called squaring
the circle. The problem is can you find a
square that has the same area as a circle. So this problem goes
way, way back. And it's a favorite problem for
amateur mathematicians. And this guy thought he had
solved the problem. But implicitly in his proof,
he had assumed that pi was exactly 3.2. Now, he was so pleased with
his proof, he wanted to copyright the proof itself so
that anyone using the proof from that point on would have
to pay him royalties. But he decided that the great
state of Indiana-- which is where he was from--
that the educational establishments of Indiana
could use it for free. How kind of him. And so what he did was he
had a bill made up. And he tried to pass it into law
that would recognize the mathematical truth that
he had discovered. But it would allow Indiana
to use it for free. Though I think he had a friend,
someone he knew, who was part of the House of
Representatives in Indiana. And he made up this bill
saying that the great mathematical truth of
squaring the circle. Now, this bill went through
committees. It went through the Education
Committee in the House of Representatives. And they obviously didn't know
what they were doing, because they passed the bill. And the representatives
actually passed it unanimously, 67 to 0. They passed it. Now, this is the weird bit. On the same day that they were
passing the bill, there was a mathematician in the building. He was there for a completely
different reason. He was a guy called
Professor Waldo. But he decided to sit in on
what they were discussing, because it was about math. So he was interested. And he couldn't believe
what he was hearing. They invited him to meet
Edwin Goodwin. Oh, do you want to meet Edwin? We're very proud of him. He said, no, I meet enough crazy
people as it is, thank you very much. So this mathematical professor
then decided to coach the Senate. The next thing that happens is
the bill goes from the House of Representatives
to the Senate. So this professor coached the
senators so that they knew what they were doing. By this time, the newspapers
had heard of it. They were mocking what
was going on. So when it reached the Senate,
they threw it out. They threw it out not before
having a bit of fun with it. They had about half an hour
of maths puns and making jokes about it. Then they threw it out. But seriously, there
are solutions-- "solutions"-- to squaring the circle, where
you take really good approximations to pi. More serious mathematicians-- for example, Ramanujan, who was
an Indian mathematician, and a brilliant one at that-- he had a solution
to this as well. So Ramanujan came up with an
approximation which meant that if you made a circle with an
area of 140,000 square miles, then you could have a square
with the same area. And the sides of the square
would be off just by an inch. So Edwin Goodwin had
done this in 1897. And you can see the documents. It's absolutely true,
this story. You can look at the documents
yourself. You can read it. And it's a strange thing
to happen, as well. Because the problem he was
trying to solve, squaring the circle, was proved to
be impossible 15 years earlier, in 1882. So I think we should have a
video about squaring the circle and what it means. BRADY HARAN: Shall we do that? DR. JAMES GRIME: Shall
we do that? BRADY HARAN: We'll film that. We're about to film it now. Tune in soon. And we'll show you about
squaring the circle. DR. JAMES GRIME: Let's have a
look at what you can do with rules and compasses. You can add numbers. Look. Here's a line. And it has length a. Then I add another
line of length b. And the whole thing
is a plus b.
You can't change pi. Legislation isn't truth.
Ok. First of all, he makes squaring the circle sound like "find the length of the side of a square which has the same area as a circle with radius r." Which is not a difficult problem at all and definitely not impossible. Second of all, I've heard this before and the story makes me mad. Maybe it's because I grew up in Indiana. I'm disappointed in you Indiana.
If this law was passed, you could use the principle of explosion to prove anything and therefore, get away with anything. Maybe this guy did know what he was doing...
He makes squaring the circle sound so cheap and rejected.
You can change what the symbol pi represents. The ratio of a circle's circumference to its diameter, however, will always be 3.14159...
Reminds me of the French Revolutionaries. During the First Republic they decided to continue France's efforts at standardising and decimalising units and measures, but to great extremes. They rewrote the calendar, giving it 12 months (with all new names) of 30 days each forming 3 10-day weeks, each day with 100 minutes, each minute with 100 seconds. Their insanity continued to also redefine angular "units" (subdivisions, really) called "grades", of which there were 400 of them in a full circle.
I should add at least a comment on why this is bad: there are a number of quantities that come in very handy when divided into "common" lots, notably multiples of 3 (and 5). One waking day is usually 2/3 of a solar cycle, since we spend 8h asleep, for instance. Angles are more often than not divided into quite a range of quantities, so having a full circle total equal to a number with a very large number of divisors is helpful.